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Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 254897, 22 pages
Research Article

Hölder-Type Inequalities for Norms of Wick Products

1Dipartimento di Matematica, Università di Bari, Campus Universitario, Via E. Orabona 4, 70125 Bari, Italy
2Department of Mathematics, Ohio State University at Marion, 1465 Mount Vernon Avenue, Marion, OH 43302, USA

Received 3 November 2007; Revised 21 January 2008; Accepted 26 February 2008

Academic Editor: Enzo Orsingher

Copyright © 2008 Alberto Lanconelli and Aurel I. Stan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Various upper bounds for the 𝐿2-norm of the Wick product of two measurable functions of a random variable 𝑋, having finite moments of any order, together with a universal minimal condition, are proven. The inequalities involve the second quantization operator of a constant times the identity operator. Some conditions ensuring that the constants involved in the second quantization operators are optimal, and interesting examples satisfying these conditions are also included.